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arXiv · 2103.07091

Hecke category actions via Smith-Treumann theory

Joshua Ciappara
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Abstract

Let $\textbf{G}$ be a simply connected semisimple algebraic group over a field of characteristic greater than the Coxeter number. We construct a monoidal action of the diagrammatic Hecke category on the principal block $\text{Rep}_0(\textbf{G})$ of $\text{Rep}(\textbf{G})$ by wall-crossing functors. This action was conjectured to exist by Riche-Williamson. Our method uses constructible sheaves and relies on Smith-Treumann theory.

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Joshua Ciappara. 2021-03-12. Hecke category actions via Smith-Treumann theory. https://arxiv.org/abs/2103.07091

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